Modeling of grain growth under fully anisotropic grain boundary energy

A level set formulation is proposed that can accurately trace the evolution of grain boundary networks in a polycrystalline aggregate while respecting grain boundary energy anisotropy. Commonly adopted simplifying assumptions related to the grain boundary energy variation with local microstructure conditions are avoided and the grain boundary energy dependence on both crystallographic misorientation and boundary plane inclination is respected. Key components in the formulation are discussed, such as an efficient and simple scheme for unequivocal identification of crystal neighbors at grain boundary junctions where an arbitrary number of crystals intersect. The method works without modifications in both two and three dimensions and is shown to provide grain boundary junction configurations that comply with classical equilibrium conditions as well as topological transforms of the grain boundary network that agree with theoretical predictions. Full grain boundary energy anisotropy is considered by adopting a parametrization of the five-parameter grain boundary energy space, as previously proposed by Bulatov et al 2014 Acta Mater. 65 161-75. Examples are provided to illustrate the relevance of the level set framework for simulations of microstructure evolution in polycrystalline solids. For example, it is clearly shown that the proposed modeling framework provides a grain boundary inclination dependence of the grain boundary energy that cannot be neglected in mesoscale simulations of grain growth.